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Financial crisis and market risk premium: Identifying multiple

structural changes

Juan J. García-MachadoProfessor of Finance, Department of Financial Economics, Accounting and Operations Management, University of Huelva (Spain). E-mail: [email protected]

Emilio CongregadoSenior Lecturer of Economics, Department of Economics and Statistics, University of Huelva (Spain). E-mail: [email protected]

Antonio A. GolpeAssistant Professor in Economics, Department of Economics and Statistics, University of Huelva (Spain). E-mail: [email protected]

Juan J. de-la-VegaSenior Lecturer of Finance, Department of Financial Economics, Accounting and Operations Management, University of Huelva (Spain). E-mail: [email protected]

abstRact: The relationship between macroeconomic variables and stock market returns is, by now, well-documented in the literature. However, in this article we examine the long-run relation-ship between stock and bond markets returns over the period from 1991:11 to 2009:11, using Bai and Perron’s multiple structural change approach. Findings indicate that while the market risk pre-mium is usually positive, periods with negative values appear only in three periods (1991:1-1993:2, 1998:3-2002:2 and from 2007:1-2009:11) leading to changes in the GDP evolution. Thereby, the study shows the presence of structural breaks in the Spanish market risk premium and its rela-tionship with business cycle. These findings contribute to a better understanding of close linkages between the financial markets and the macroeconomic variables such as GDP. Implications of the study and suggestions for future research are provided.

KeywoRds: Financial crisis, market risk premium, risk free rate, Spanish financial markets, Spanish government bonds, structural change.

IntroductIon1

in an article entitled europeans start to worry that U.s. fever could be conta-gious, the Financial Times warned that: “this was the week when the finan-cial crisis and its ripple effects finally spread out of the banking sector and reverberated through the rest of corporate europe” (milne & Guerrera, 2008, p. 16). By may 2008, the european Central Bank indicated that “demand for eurozone bank loans has tumbled and credit standards have tightened

1 this procedure has a number of advantages over previous approaches (for details, see Bai and Perron, 2006).

153

crisis financiera y Prima De riesgo De mercaDo: iDentificanDo cambios estructurales múltiPles

resumen: La relación entre variables macroeconómicas y los rendimientos del mercado bursátil está bien documentado en la literatura. Sin embargo, en este artículo examinamos la re-lación a largo plazo entre los rendimientos de los mercados de bonos durante el periodo 1991:11 - 2009:11, utilizando la me-todología de cambios estructurales propuesta por Bai y Perron. Nuestros hallazgos indican que, mientras que la prima de riesgo es comúnmente positiva, aparecen tres períodos en los que ésta toma signo negativo (1991:1-1993:2, 1998:3-2002:2 and from 2007:1-2009:11) adelantando cambios en la evolución del PIB. De esta forma, el estudio muestra la existencia de cambios es-tructurales en la prima de riesgo española y la relación de ésta con el ciclo económico. Estos resultados contribuyen a una me-jor comprensión de las estrechas relaciones entre los mercados financieros y el entorno macroeconómico. El trabajo también analiza las implicaciones del estudio así como sugerencias para la investigación futura.

Palabras clave: crisis financiera, prima de riesgo, tipo sin ries-go, mercados financieros, bonos del Estado, España, cambio es-tructural.

crise financière et Prime De marché: iDentification De changements structurels multiPles

résumé : La relation entre les variables macroéconomiques et les rendements du marché boursier a bien été documentée dans les publications antérieures. Cependant, cet article examine la relation à long terme entre les rendements des marchés de bo-nus durant la période de 1991/11 à 2009/11, par la méthodo-logie des changements structurels proposée par Bai et Perron. Les résultats indiquent que, bien que la prime de risque soit gé-néralement positive, elle est négative durant trois périodes (de 1991/1 à 1993/2, de 1998/3 à 2002/2 et de 2007/1 à 2009/11), entraînant des changements dans l’evolution du PIB. L’etude effectuée démontre l’existence de changements structurels concernant la prime de risque espagnole et son rapport avec le cycle économique. Ces résultats contribuent à une meilleure compréhension des relations étroites entre les marchés finan-ciers et le cardre macroéconommique. L’article analyse égale-ment les implications de l’étude et fournit des propositions pour la recherche future.

mots-clefs: crise financière, prime de risque, type sans risque, marchés financiers, bonus de l’Etat, changement structurel.

crise financeira e Prima De risco De mercaDo: iDentificanDo múltiPlas muDanças estruturais

resumo: A relação entre variáveis macroeconômicas e os ren-dimentos da bolsa de valores está bem documentado na litera-tura. Sem embargo, neste artigo examinamos a relação a longo prazo entre os rendimentos dos mercados de bônus durante o período 1991:11 - 2009:11, utilizando a metodologia de múlti-plas mudanças estruturais proposta por Bai e Perron. Nossas descobertas indicam que, enquanto que a prima de risco e co-mumente positiva, aparecem três períodos nos que esta se tor-na negativa (1991:1-1993:2, 1998:3-2002:2 e 2007:1-2009:11) adiantando mudanças na evolução do PIB. Desta forma, o es-tudo mostra a existência de mudanças estruturais na prima de risco espanhola e a relação desta com o ciclo econômico. Estes resultados contribuem a uma melhor compreensão das estrei-tas relações entre os mercados financeiros e o entorno ma-croeconômico. O trabalho também analisa as implicações do estudo assim como apresenta sugestões para a pesquisa futura.

Palavras chave: crise financeira, prima de risco, tipo sem ris-co, mercados financeiros, bônus do Estado, Espanha, mudança estrutural.

clasificación Jel: G11, G12, C32, E44.

recibiDo: diciembre de 2009 aProbaDo: noviembre de 2010

corresPonDencia: Juan J. García-Machado. Depto. de Economía Fi-nanciera, Contabilidad y Dirección de Operaciones. Facultad de Ciencias Empresariales. Plaza de la Merced, 11, E-21001, Huelva, España. .

citación: García-Machado, J., Congregado, E., Golpe, A. A. & De-la-Vega, J. J. (2011). Financial crisis and market risk premium: identifying multiple structural changes. Innovar, 21(39), 153-160.

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further, according to a european Central Bank survey that could dent confidence in the region’s resilience” (Atkins, 2008, p. 2).

For at least two decades, the european Union (eU) had lagged behind the United states in regard to economic growth and productivity improvements. meanwhile, the european financial markets were still not integrated, and each nation still had its own regulatory standards.

some academics remained pessimistic about the future growth in europe, suggesting that the traditional forces of government regulation and ownership, expensive social security systems, and high taxes would place a growing burden on all european countries, thereby constricting fi-nancial oportunities. an important reality was that U.s. GdP was nearly 25% of global GdP, so a change in U.s. economic activity would inevitably have ripple effects throughout the world. the 2007-2008 financial crisis has demonstrated the close linkages between the financial system and the economy as a whole (Conklin and Cadieux, 2008, p. 12).

With regard to market risk premium, this is one of the most important numbers in finance. Unfortunately, estimating and understanding its value has proved to be difficult. al-though a substantial body of research shows that expect-ed returns vary over time, the static approach of estimating the risk premium as the simple average of historical excess stock returns remains the most commonly employed meth-od in practice (mayfield, 2004, pp. 465-466).

in spain, market risk premium has experienced a remark-able turnaround in the last three years. in particular, posi-tive market risk premium values during the most part of the 1990’s and 2000’s have turned into negative ones after 2007:1.

this situation was expected as prior to the current finan-cial crisis, with the booming stock market and promising return from stock market, people were inclined to invest in this market with the expectation to achieve a quick benefit within a short period.

it is a well-known fact that the relationship between stock and bond markets –among different types of assets– plays an important role in asset allocation strategies and port-folio diversification process. Given that, the stock and the bond market are interdependent, dynamic allocation of funds from one market to another is possible, which in turn will result in balanced price increase in the bond market and in declining price in the stock market.

in particular, the strategic allocations of capital resources between stocks and bonds and the degree of correlation

between them is one of the most important elements that determine portfolio performance, given that stock and bond market are closed substitute for balancing of port-folio of assets.

the dynamic nature of this asset allocation has been stud-ied from different perspectives. Recent works have ex-plored the long-run relationship between these two classes of asset using co-integration analysis (ahmed, 2009; Clare et al., 1994; mills, 1991). However, we will try to analyze this relationship from a different perspective: testing the existence of structural changes in the risk market premium and showing that this allocation pattern changed during 2007 anticipating the current credit crunch.

therefore, the objective of this study is two folds: Firstly, this study aims to examine the strategic (long-term) rela-tionship between stock and bond markets returns identify-ing structural changes using the approach developed by Bai and Perron (1998, 2003a). this procedure will allow us to test endogenously for the presence of multiple struc-tural changes in this relationship.2 secondly, given close interdependence of these two markets and the macroeco-nomic performance we will try to show in an informal way if these structural changes have acted as leading indica-tors to business cycles.

the rest of the article is organized as follows: section 2 rep-resents a selective review of the premium risk concept and some previous related empirical literature on the relation-ship between stock and bond markets. section 3 briefly describes the data and methodology, whereas section 4 shows our main results. Finally, conclusions and implica-tions are presented in section 5.

tHeoretIcal BacKground

many of available studies show the relationship between the financial markets and the macroeconomic variables. For example, Cooper et al. (2004) examine the cointegra-tion between macroeconomic variables and stock market indices from singapore stock exchange. Hördahl (2008) uses a dynamic term structure model based on an explicit structural macroeconomic framework to estimate inflation risk premium in the United states and the euro area.

moreover, a lot of researches show that expected returns vary over time. For example, Fama and schwert (1977), shiller (1984), Campbell and shiller(1988), Fama and French (1988, 1989), Campbel (1991), Hodrick (1992) and

2 this procedure has a number of advantages over previous appro-aches (for details, see Bai and Perron, 2006).

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lamont (1998). Brunner et al. (1998) survey a sample of 27 “highly regarded corporations” and find that the esti-mates of risk premium are generally based on either the arithmetic or geometric average of historical excess mar-ket returns.

Recent studies provide historical evidence of a structural shift in the market risk premium. siegel (1992) documents that the market premium has not been constant over the past century and the excess stock returns during the mid-1900s are abnormally large. Pastor and stambaugh (2001) use a Bayesian analysis to test for structural breaks in the distribution of historical returns and to relate those breaks to changes in the market risk premium. Fama and French (2002) provide evidence of a structural shift in the market risk premium by comparing the ex-ante risk premium from a Gordon growth model with the ex-post risk premium based on the historical average of excess market returns. evidence of a structural shift in the volatility of market re-turns is also provided in earlier studies. officer (1973) and schwert (1989) argue that market returns during the Great depression era were unusually volatile, and Pagan and schwert (1990) show that the volatility of market returns during the Great depression was inconsistent with station-ary models of heteroskedastic returns. mayfield (2004) provides a model with a structural basis for estimating the

impact of such a structural shift on the market risk premium. Consistent with Pagan and schwert (1990) and Pastor and stambaugh (2001), mayfield found evidence of a statisti-cally significant shift in the underlying volatility process that governs the evolution of volatility states following the 1930s. Because of the structural shift in the markov transi-tion probabilities, the likelihood of entering into the high-volatility state falls from about 39% before 1940 to less than 5% after 1940. Given the lower likelihood of entering the high-volatility state, the risk premium falls from about 20.1% before 1940 to 7.1% after 1940 (mayfield, 2004, p. 468).

Further, given the assumed market efficiency in stock and bond market, no arbitrage relationship is expected from these two markets. the formation of such relation can be explained as:

premiumriskmarketBESE ϑϑ (1)

where θ is the set of information. therefore the expected return on stock depends on expected return on bond plus additional risk premium in relation to the bond. it is as-sumed that, over the years, information set is likely to be changed given the dynamic economics environment which could lead to changes in risk premium rather than being held constant. therefore the marginal investor may like to



take in and out money from these two markets until we have equilibrium relationship of stock and bond markets. in sum, stock market uncertainty could be important for cross-market pricing influences and should be taken into consideration when setting optimal portfolio allocations (Connolly et al., 2005).

this relationship has been extensively explored. For in-stance, lo and macKinlay (1988) or Fama and French (1996) show that stock and bond returns do not follow a random walk process. Further support to this finding can be founded in Fleming and Remolona (1997), Clare and thomas (1992), Campbell and Hamao (1989), and Keim and stambaugh (1986). a second class of empirical works are focused on the co-movement and causality between stocks and bonds (Chordia et al., 2005; Fleming et al., 1998; Hotchikiss and Ronen, 2002; li, 2002; li and Zou, 2008 Wainscott, 1990) whereas the most recent research has looked for co-integration between stock and bond in-dexes (ahmed, 2009; Clare et al., 1994; mills, 1991).

in general, evidence suggests that correlation between stock and bond return may play a crucial role in allocation decisions leading to movements in some key macroeco-nomic variables. Chan et al. (1997) studied whether stock and bond prices were collinear in the long run. the results of the unit root tests suggested that the bond and the stock markets were integrated of the first order. therefore, a nonstationary component was driving these stock and bond prices. they found that this nonstationary compo-nent was not shared by the two prices, indicating that the two prices could move apart over time.

data and metHodology

the empirical analysis data uses monthly data on stock and bond spanish markets taken from the spanish Cen-tral Bank.3 to operationalize the concept of market risk premium, we decided to use the concept of historical risk premium,4 defining it as the historical differential return of

3 asset markets time series. in particular the two time series con-sidered are the treasury bond (10 years) average return and the madrid General stock index (iGBB, Bolsa de madrid). data were downloaded from the Biest (spanish Central Bank time series search engine) collected by spanish Central Bank on december, 2009. available at: http://app.bde.es/tsi_www/paginaBienveni-da.do?idioma=es [04/12/09]. Data on Spanish real GDP are tak-en from the quarterly national accounts database available at: http://www.ine.es/jaxiBD/tabla.do?per=03&type=db&divi=CNTR&idtab=9 [04/12/09].

4 the concept of market risk premium can be considered from alter-native perspectives. For instance, as the incremental return of the market over the return of treasury bonds required by an investor–required market risk premium–or alternatively as the expected dif-

the stock market over treasury bonds. therefore, the mar-ket risk premium is calculated as the difference between the stock return (Rmsi) and the risk free return or treasury bond return (Rsb):

tt RsbRmsipremiumriskmarket −

(2)

to calculate Rmsi, we take natural logarithm on the mon-thy madrid stock market index in first-difference, multiply-ing it by 12 to transform our original data in annual rates. Rsb is the risk free return expressed as annual rates.

as we mentioned, an alternative though indirect way of analyzing the relationship between stock and bond market returns is by means of the market risk premium evolution, testing the presence of structural changes in the spanish market risk over the period 1991:1-2009:11.

as suggested above, we examine the possibility of in-stabilities in this relationship to address the question of whether the long-run relationship estimated between stock and bond market returns is stable over time or it exhibits some structural break allowing the instability to occur at a unknown date. to carry out this task we use the tests of multiple structural breaks proposed by Bai and Perron (1998, 2003).

Bai-Perron’s approach allows to test for multiple breaks at unknown dates, so that it successively estimates each break point by using a specific-to-general strategy to de-termine the number of breaks. Bai and Perron (1998) sug-gest several statistics to indentify the break points: i) the kSupFt test, i.e. a sup F-type test of the null hypothesis of non structural break vs the alternative of a fixed (arbi-trary) number of breaks estimating the long-run relation-ship with multiple structural breaks k; ii) two maximum test of the null hyothesis of no structural break vs the al-ternative of a unknown number of breaks given some up-per bound, i.e. UD

max test, an equal weighted version, and

WDmax

test, with weights that depend on the number of regressors and the significance level of the test; and iii) the 1tSupF test, i.e. a sequential test of the null hypothesis of breaks vs the alternative 1 of breaks.

results

We begin our analysis by examining the time-series proper-ties of the series. We use a modified version of the dickey and Fuller (1979, 1981) test (dF) and a modified version of the Phillips and Perron (1988) tests (PP) proposed by

ferential return of the stock market over treasury bonds –expected market risk premium–. see Fernández (2009) for a detailed discus-sion.

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ng and Perron (2001) for the null hypothesis of a unit root to solve the traditional problems associated to convention-al unit root tests. ng and Perron (2001) propose a class of modified tests, M , with Gls detrending of the data and using the modified akaike information criteria to select the autoregressive truncation lag.

table a1 reports test statistics of ng-Perron tests, GLSZM α , GLS

tZM , GLSSBM , GLSPTM . all test statistics formally exam-ine the unit root null hypothesis against the alternative of stationarity. at the 5% level, the null hypothesis of non-stationarity for the series in levels for Rmsi and Rsb cannot be rejected by using ng-Perron tests. By contrast, however both adF and KPss tests suggest that the two series are stationary.

the results of applying the Bai-Perron tests to the relation-ship between stock and bond market are shown in table 2. to estimate the partial structural change model we con-sider a particular specification with serially uncorrelated errors, different distributions for the data across segments and the same distribution for the errors across segments.

We allowed up to eight breaks and used a trimming of ε = 0.10, so that each regime has at least 22 observations. We apply the procedure with a constant and account for potential serial correlation via non-parametric adjustments. the statistics UD

max and WD

max are highly significant which

implies that at least one break in the model exists. as we can see, all the kSupFt tests are significant with k run-ning between one and eight so that at least one break could be present in this relationship. in turn, 1tSupFthe test is not significant for any 7≥ , so the sequential procedure selects six breaks. Hence, the results of the Bai-Perron tests would suggest a model of seven regimes, with the dates of the breaks estimated at July 1993, october 1996, July 1998, august 2002, october 2004 and decem-ber 2006 (their confidence intervals are shown in table 1).

Finally, we proceed to estimate the market risk premium for the seven sub-samples and the results are shown in the columns of table 3. as it can be seen, in the first, fourth and last regime the market risk premium is negative. Com-paring these regimes with the evolution of the GdP we can observe the similar pattern followed by these markets and

taBle 1. unit root tests

Variable ADF Lags KPSS GLSZM α GLS

tZM GLSSBM GLSPTM Lags

stock market -3,880* 9 0,131 -2,483 -1,105 0,445 9,818 8

treasure bond -2,577*** 10 0,345 -0,313 -0,202 0,647 25,663 3

*Denotes hull hypothesis rejection. Remember that the null hypothesis in the KPSS test is stationarity whereas the null in the rest of the test is the existence of a unit root.

taBle 2. Bai-Perron tests of multiple structural changes in the long-run relationship

specifications

yt={Rmsi

t} z

t={1,Rsb

t} q=2 p=0 h=22 m=8

tests

UDmax

WDmax

1032,164* 1196,133*SupFt(1) SupFt(2) SupFt(3) SupFt(4) SupFt(5) SupFt(6) SupFt(7) SupFt(8)

1032,164* 777,572* 907,715* 707,018* 569,277* 506,238* 455,373* 387,510*

SupFt(2/1) SupFt(3/2) SupFt(4/3) SupFt(5/4) SupFt(6/5) SupFt(7/6) SupFt(8/7)

194,546* 34,129* 28,594* 24,328* 24,328* 20,935 0,000

Break dates estimates

t1

1993:07 [1993:01-1993:09]

t2

1996:10 [1996:09-1996:11]

t3

1998:07 [1998:05-1998:11]

t4

2002:08 [2002:07-2002:11]

t5

2004:10 [2004:08-2004:11]

t6

2006:12 [2006:10-2007:02]

Notes: yt,zt,q,p,h, and M denote the dependent variable, the explanatory variables allowed to change, the number of regressors, the number of corrections included in the variance-covariance matrix, the

minimum number of observations in each segment, and the maximum number of breaks, respectively.

***,**,and * denote significance at the 10%,5% and 1% levels, respectively. The critical values are taken from Bai and Perron (1998), Tables 1 and 2; and from Bai & Perron (2001), Tables 1 and 2.

The number of breaks (in our case, seven) has been determined according to the sequential procedure of Bai and Perron (1998), at the 1% size for the sequential test 1tSupF .

95% confidence intervals for Ti in brackets.



the recent macroeconomic evolution (see, Figure 1). table 3 also includes both the anova F test and the Barlett test for testing the equality of means and variances between regimes. in both cases, results reject the null hypothesis of equality of means and variances, respectively between the regimes.

in the figure 1, shadow areas corresponds to regimes with negative market risk premium (regimes 1, 4 and 7). as we can observe these regimes corresponds to a deaccelaration or crises episodies. in this sense, structural changes in the evolution of the market risk premium lead to changes in the business cycle.

conclusIons

this paper tested the presence of structural breaks in the spanish risk market premium and its relationship with business cycle. defining market risk premium in terms of the difference between the stock return and the risk free return or treasury bond return, the results provide robust evidence of structural changes leading to business cycles changes. in particular, our findings indicate that while the market risk premium is usually positive, periods with neg-ative values appear only in three periods (1991:1-1993:2, 1998:3-2002:2 and from 2007:1-2009:11) leading to changes in the GdP evolution. therefore, the strategic

taBle 3. risk premium across different regimes (annual).

Full sample First regimesecond regime

thrid regimeFourth regime

Fifth regime sixth regimeseventh regime

1991:11-2009:10

1991:11-1993:05

1993:06-1996:09

1996:10-1998:06

1998:07-2002:07

2002:08-2004:09

2004:10-2006:11

2006:12-2009:11

average Risk premium 2,124 -12,467 0,672 43,816 -12,368 7,793 23,219 -12,528

volatility 68,924 63,133 58,479 73,429 77,918 64,675 36,509 77,952

skewness -0.536 -0.422 0.156 -0.811 -0.383 -0.849 -0.435 -0.567

Kurtosis 4.035 1.996 2.525 3.625 4.149 4.678 2.875 3.726

Jarque Bera test 0.000 0.489 0.769 0.266 0.142 0.046 0.658 0.267

test for equality of means between regimesanova F- test df(6,209) P-value in brackets

2,604 [0,019]

Barlett test for equality of variances between regimes Barlett test df(6) P-value in brackets

18,477 [0,005]

Note: In cursive regimes with negative market risk premium.

FIgure 1. the evolution of gdP in market risk Premium regimes.

1991IV1992II1992IV1993II1993IV1994II1994IV1995TII1995TIV1996TII1996TIV1997TII1997TIV1998TII1998TIV1999TII1999TIV2000TII2000TIV2001TII2001TIV2002TII2002TIV2003TII2003TIV2004TII2004TIV2005TII2005TIV2006TII2006TIV2007TII2007TIV2008TII2008TIV2009TII

GDP Growth

Regime 1 Regime 2 Regime 3 Regime 4 Regime 5 Regime 6 Regime 7

-2

-1,5

-1

-0,5

0

0,5

1

1,5

2

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allocations of capital resources between stocks and bonds as two close substitutes for balancing of portfolio of as-sets must be considered a way to anticipate changes in business cycles’ phases, given that stock market uncer-tainty has important cross-market pricing influences and should be taken into consideration when setting optimal portfolio allocations.

this result also suggests that forecasting of financial re-turn series are subject to breaks and advises us on the presence of certain correlation between these breaks in the movement among stock and bond indices and macro-economic variables. in view of evidence that these structur-al changes and regime shifts seem to lead business cycle turningpoints, the use of the link between stock and bonds returns and its structural breaks as a predictor of economic crises would be present in the future research agenda, to test the potential to increase the out-of-sample predict-ability of GdP.

However, we cannot rule out the possibility that it might simply reflect data limitations given that our analysis fo-cuses on a singular country.5 therefore, future work might fruitfully apply the methodology used in this article to a broader range of countries and should also seek to extend the length of the data series which are utilized.

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